Federated learning (FL) approaches for saddle point problems (SPP) have recently gained in popularity due to the critical role they play in machine learning (ML). Existing works mostly target smooth unconstrained objectives in Euclidean space, whereas ML problems often involve constraints or non-smooth regularization, which results in a need for composite optimization. Addressing these issues, we propose Federated Dual Extrapolation (FeDualEx), an extra-step primal-dual algorithm, which is the first of its kind that encompasses both saddle point optimization and composite objectives under the FL paradigm. Both the convergence analysis and the empirical evaluation demonstrate the effectiveness of FeDualEx in these challenging settings. In addition, even for the sequential version of FeDualEx, we provide rates for the stochastic composite saddle point setting which, to our knowledge, are not found in prior literature.

翻译：联邦学习中的鞍点问题近年因在机器学习中的关键作用而备受关注。现有研究主要针对欧氏空间中平滑无约束目标，但机器学习问题常涉及约束或非平滑正则化，这需要复合优化方法。针对上述问题，我们提出联邦对偶外推（FeDualEx）算法——一种额外步原始-对偶算法，这是联邦学习范式下首个同时涵盖鞍点优化与复合目标的方法。收敛性分析与实验评估均证明了FeDualEx在复杂场景下的有效性。此外，即便对于FeDualEx的序贯版本，我们首次给出了随机复合鞍点场景下的收敛速率，据我们所知，这在既往文献中尚未出现。